Welcome to Little Melton Primary

School

Calculations Addition and Subtraction

2011

This evening we will:• Outline the features of our calculations policy.• Focus on the strategies used to develop the children’s understanding and application of addition and subtraction.• Identify key areas where you can help your child with their maths.• Share classroom resources and approaches.

• And of course – DO SOME MATHS!

What can a numerate child do?

By the age of 11 they should:• Have a sense of the size of number and where it fits into the number system.• Know by heart addition and subtraction facts to 20, multiplication and division facts to 10 x 10, doubles and halves, complements to 100, multiply and divide by 10 and 100.

• Use what they know to figure out answers mentally.• Calculate accurately and efficiently, both mentally and on paper, using a range of strategies.• Recognise when it is appropriate to use a calculator (and when it is not) and be able to use one effectively.• Explain their methods and reasoning using correct mathematical terms.• Judge whether their answers are reasonable and have strategies for checking them where necessary.

• The aim is for children to do mathematics in their heads, and if the numbers are too large, to use pencil and paper methods to avoid losing track.• To do this children need to learn quick and efficient methods, including appropriate written methods.

Learning written methods is not the ultimate aim.•Our maths teaching aims to develop children’s mental strategies and then written methods that derive from and support these mental methods.

We want the children to ask themselves:• Can I do this in my head?• Can I do this in my head using drawings or jottings?• Do I need to use a pencil and paper procedure?

• Do I need a calculator?

Calculations policy Our school Calculations policy shows how the methods progress across the year groups. Some children may be ready for the year appropriate method, others may be consolidating the previous year’s or being extended.

How do you add and subtract?

61 + 45

83 - 68

5735 + 3657

538 -295

7800 -5600

5735 + 3990

5002 - 4996

267 + 267 362 + 39

2.5 + 2.7 5.1 – 2.78

Addition – Early stages• Practical activities and

discussions. Recognising numbers. Count objects up to 10. Find one more than a number. Count in ones and tens. Relate addition to combining two groups of objects. Count along a number line to add numbers. Begin to use + and = signs in a number sentence.

Addition – Mid stages•Mental Strategies and Informal Methods Looking for pairs that make 10 then 20, 30 etc.

16 + 12 + 4=

Using a number square, count on the units then the tens. Adding ‘nearly’ numbers – To add 9 add 10 then subtract 1

32 + 9 = 32 +10 = 42 -1 = 41

Using a number line, bridging through a multiple of 10 e.g 27 + 8

+3 +5 _______________________________________________

27 30 35

Addition – Mid stages• Formal Methods start to emerge: Add using partitioning: 47 + 34 = 40 + 7 +30 + 4= Add units 4 + 7 = 11 Add tens 40 + 30 = 70 Total 70 + 13 = 81

Expanded Method: 47 + 34 = TU 47 34 11 (7 + 4) 70 (40 + 30) 81

Addition – Later stages• Standard Methods Label columns and carry below the line:

Th H T U H T U . t h 3 5 8 7 1 2 4 . 9 0 + 6 7 5 + 1 1 7 . 2 5 4 2 6 2 2 4 2 . 1 5 1 1 1 1 1

Now it is your turn!• Try using one of the methods

shown to answer these:1. I have £257 in one bank account and

£468 in another. How much is there altogether?

2. A sunflower measures 1.94m. By Friday it has grown 38cm. How tall is it now?

Subtraction – Early stages

• Practical activities and discussion Count backwards in number rhymes or stories. Count back from a given number. Begin to relate subtraction to take-away. Find one less than a number.Counting back in tens.Count backwards along a number line to take away.Begin to use the – and = signs to record mental subtractions.

Subtraction – Mid stages• Mental Strategies and Informal

Methods Using a number square, partition the number, then count back the units then the tens. Subtracting ‘nearly’ numbers – To take 9 take 10 then add 1

32 - 9 = 32 -10 = 22 +1 = 23

Using a number line, bridging through a multiple of 10 e.g 63 – 26

37 47 57 60 63 -10 -10 -3 -3

Recognise when to count on: when 2 numbers are close together e.g.106 – 98 + 2 + 6 = 8

_________________________ 98 100 106

Subtraction – Mid stages• Methods which lead to Standard

Methods Can also use counting on:

+22 +100 +74 = 196 374

- 178 ___________________________________ 178 200 300 374 Expanded Method – Exchanging 10 43 – 27 = T U T U 40 + 3 30 + 13 20 + 7 20 + 7 10 + 6 = 16 • This leads to understanding how the standard written method works.

Subtraction – Later stages

•Standard methods Complementary addition e.g. 6467 – 2684 = 3783

2684 + 16 (2700) can be refined to + 316 (3000) + 300 (3000) + 3467 (6467) + 3467 (6467) 3783 = 3783 Standard decomposition layout will be introduced via partitioning into HTU where exchange can be clearly shown.

Now it is your turn again!

• Try using one of the methods shown to answer these:

1. There are 83 children on the playground. 37 go in for their

lunch. How many are left outside?

2. A sports stadium holds 9010 spectators. 5643 people attend a football match. How many empty seats are there?

This evening we will:• Outline the features of our calculations policy.• Focus on the strategies used to develop the children’s understanding and application of multiplication and division.• Identify key areas where you can help your child with their maths.• Share classroom resources and approaches.

• And of course – DO SOME MATHS!

How do you multiply and divide?

57 x 2

742 ÷ 2

78 ÷ 2

36 x 25

18 x 15

43 x 50

700 ÷ 4

5.4 ÷ 6 8 x 19

17 ÷ 5 34 x 7

Multiplication – Early stages• Practical activities and

discussions. Counting in twos, fives and tens.

Using activities to recognise doubles and halves.

Using equipment to give lots of practice of making groups.

Multiplication – Mid stages•Mental Strategies and Informal Methods Using arrays. ●●●● 2 x 4 means 2 lots of / groups of 4 ●●●● 2 x 4 = 8 OR 4 x 2 is 4 lots of / groups of 2 ●● 4 x 2 = 8 * Therefore demonstrating ●● that multiplication can be ●● done in any order. ●●

Partitioning e.g. 4 x 13 = 4 x 3 = 12 4 x 10 = 40 Total 12 + 40 = 52

Counting on using times tables. They really need to know tables!!

Multiplication – Later stages• Methods which lead to Standard Methods Use what is already known to help with what is not known: if 3 x 4 = 12 then 30 x 4 = 120 and 30 x 40 = 1200 7 x 0.8 = we know 7 x 8 = 56 therefore 10 x smaller = 5.6

The grid method:1, First partition and put numbers in grid2, Multiply each number together, remembering to use existing knowledge.3, Total each row or column and then add together.

= 13040

= 652 Total = 13692

x 300

20 6

40 12000

800 240

2 600 40 12

Multiplication – Later stages• Standard Methods Short multiplication Long multiplication H T U H T U 4 8 6 7 x 7 x 3 6 5 6 (7 x 8) 4 2 (6 x 7) 2 8 0 (7 x 40) 3 6 0 (6 x 60) 3 3 6 2 1 0 (30 x 7)

1 8 0 0 (30 x 60) 2 4 1 2

Extend to decimals with up to two decimal places. Higher attaining children will move to formal methods of multiplication carrying numbers underneath..

Now it is your turn!• Try using one of the methods

shown to answer these:1. How many legs do 36 spiders have?2. A concert hall has 124 rows of chairs,

each row has 32 chairs. How many chairs are there altogether?

Division – Early stages• Practical activities and discussion Counting back in tens, twos and fives.

Know halves ... half of 6 is 3

Division – Mid stages• Mental Strategies and Informal Methods Counting on and back using tables. Understanding division as sharing e.g If 20 sweets are shared between 4 people how many will each get?

Understanding division as grouping e.g. How many groups of 5 are there in 20? (Use apparatus and tables)

Using arrays: 10 divided into 2 groups = 5 in each group

●●●●● ●●●●●

OR 10 divided into 5 groups = 2 in each group

●● ●● ●●

●● ●●

Division – Mid stages• Methods Strategies and Informal Methods Repeated subtraction: 12 ÷ 3 means how many 3’s in 12, therefore keep

subtracting 3’s 12 - 3 = 9, 9 – 3 = 6 etc. __-3____-3____-3____-3___ How many 3’s? = 4

0 3 6 9 12

Start to understand remainders and if you need to round up or down. e.g If I have 14 eggs, how many egg boxes will I need? 14 ÷ 6 = 2 remainder 2

2 full egg boxes and 2 in the other Answer = 3 egg boxes

Division – Mid stages• Methods Strategies and Informal Methods Chunking - Use times tables and partitioning:

93 ÷ 6 =60 ÷ 6 = 10 (partition 93 using 6x table knowledge)33 ÷ 6 = 5 r3= 15 r 3

977 ÷ 36 = 977 - 720 (20 x 36)

257 - 180 (5 x 36)

77 - 72 (2 x 36)

5 Answer = 27 r5 Extend to 4 digit numbers and decimals. Introduce ‘bus shelter’ when secure.

Now it is your turn again!

• Try using one of the methods shown to answer these:

1. 72 children were put into teams of 6 for sports day. How many teams were there?

2. 168 children and 19 adults are going on a school trip.

Each minibus holds 15 passengers. How many minibuses will be needed?

Remember:How did you do

it?

Can you explain the method you

used?

Which method did you

use?

What skills were you

using?

Will this method work

for all of these

calculations?

Talk me through

your workings.

How can you help at home?Talk about

how you do maths.

Give praise and

encouragement.

Ask your child to explain.

Be positive!

Make sure maths is fun!

Booklets for parents • Helping your child with addition, subtraction, multiplication and division.

Thank you for attending – your

interest means a lot to us and your children!